When you see X ⊃ Y, you are to read "X implies Y" or "If X, then Y." Sometimes you may see the modern form, X —> Y, in my comments.
When you see X ≡ Y, you should read "X equivalent to Y" or "X strictly implies Y" or "If and only if X, then Y" or "If X, then Y and if Y, then X" (these forms are sometimes shortened to "iff"). "X ≡ Y" can also be read: "Y is necessary for X and X is sufficient for Y." Occasionally one also sees "X ≡ Y" interpreted as "Y holds just in case X holds" or "Y holds only in case X holds" and the converse, "X holds just in case Y holds." Sometimes my comments use the modern X <—> Y.
For the quantifier all, you will see ( ), as in (x)Fx. In my comments I sometimes use the modern symbol ∀, as in ∀xFx. The existential quantifer ∃, as in ∃xFx, is used in W's text and in my comments. P●Q should be read "P and Q." Often the dot is dropped, as in PQ. Occasionally dots are used instead of parentheses.
2
What is the case, the fact, is the existence of atomic facts.
2.01
An atomic fact is a combination of objects (entities, things).
2.011
It is essential to a thing that it can be a constituent part of an atomic fact.
2.012
In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.
2.0121
It would, so to speak, appear as an accident, when to a thing that could exist alone on its own account, subsequently a state of affairs could be made to fit.
If things can occur in atomic facts, this possibility must already lie in them.
(A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.)
Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connection with other things.
If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context.
2.0122
The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connection with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.)
2.0123
If I know an object, then I also know all the possibilities of its occurrence in atomic facts.
(Every such possibility must lie in the nature of the object.)
A new possibility cannot subsequently be found.
What is the case, the fact, is the existence of atomic facts.
2.01
An atomic fact is a combination of objects (entities, things).
2.011
It is essential to a thing that it can be a constituent part of an atomic fact.
2.012
In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.
2.0121
It would, so to speak, appear as an accident, when to a thing that could exist alone on its own account, subsequently a state of affairs could be made to fit.
If things can occur in atomic facts, this possibility must already lie in them.
(A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.)
Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connection with other things.
If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context.
2.0122
The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connection with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.)
2.0123
If I know an object, then I also know all the possibilities of its occurrence in atomic facts.
(Every such possibility must lie in the nature of the object.)
A new possibility cannot subsequently be found.
I interpret this thus: Any object -- or its representation -- is a member of some relation. Hence, the object implies all the relations of which it is a member.
By relation I mean the subset Ri< a,b >. If a is the object, then there is may be a subset in which b varies. We also have other relations, as in Rj< a,b >. So he is saying, I suppose, that all the relevant b's and R's are implied.
I note that W. is not always clear as to the distinction between an object and its representation. Of course, in the idealist and semi-idealist view (as for example in my paper Toward a Signal Model of Perception), the lines blur between exterior and mental object, between object and concept).
By relation I mean the subset Ri< a,b >. If a is the object, then there is may be a subset in which b varies. We also have other relations, as in Rj< a,b >. So he is saying, I suppose, that all the relevant b's and R's are implied.
I note that W. is not always clear as to the distinction between an object and its representation. Of course, in the idealist and semi-idealist view (as for example in my paper Toward a Signal Model of Perception), the lines blur between exterior and mental object, between object and concept).
2.01231
In order to know an object, I must know not its external but all its internal qualities.
2.0124
If all objects are given, then thereby are all possible atomic facts also given.
2.013
Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.
2.0131
A spatial object must lie in infinite space. (A point in space is an argument place.)
A speck in a visual field need not be red, but it must have a colour; it has, so to speak, a colour space round it. A tone must have a pitch, the object of the sense of touch a hardness, etc.
2.014
Objects contain the possibility of all states of affairs.
2.0141
The possibility of its occurrence in atomic facts is the form of the object.
2.02
The object is simple.
In order to know an object, I must know not its external but all its internal qualities.
2.0124
If all objects are given, then thereby are all possible atomic facts also given.
2.013
Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.
2.0131
A spatial object must lie in infinite space. (A point in space is an argument place.)
A speck in a visual field need not be red, but it must have a colour; it has, so to speak, a colour space round it. A tone must have a pitch, the object of the sense of touch a hardness, etc.
2.014
Objects contain the possibility of all states of affairs.
2.0141
The possibility of its occurrence in atomic facts is the form of the object.
2.02
The object is simple.
These objects are primitives, rather like Leibniz's monads, except of course W. has not souls in mind.
2.0201
Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.
2.021
Objects form the substance of the world. Therefore they cannot be compound.
2.0211
If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.
2.0212
It would then be impossible to form a picture of the world (true or false).
2.022
It is clear that however different from the real one an imagined world may be, it must have something—a form—in common with the real world.
2.023
This fixed form consists of the objects.
Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.
2.021
Objects form the substance of the world. Therefore they cannot be compound.
2.0211
If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.
2.0212
It would then be impossible to form a picture of the world (true or false).
2.022
It is clear that however different from the real one an imagined world may be, it must have something—a form—in common with the real world.
2.023
This fixed form consists of the objects.
So does W. means mental objects or physical things "out there in the real world" in a form of naive realism?
I suppose he is in effect saying that what imaginary and real worlds have in common are what might be called thought forms, or just thoughts, or concepts.
I suppose he is in effect saying that what imaginary and real worlds have in common are what might be called thought forms, or just thoughts, or concepts.
2.0231
The substance of the world can only determine a form and not any material properties. For these are first presented by the propositions—first formed by the configuration of the objects.
2.0232
Roughly speaking: objects are colourless.
2.0233
Two objects of the same logical form are—apart from their external properties—only distinguished from one another in that they are different.
The substance of the world can only determine a form and not any material properties. For these are first presented by the propositions—first formed by the configuration of the objects.
2.0232
Roughly speaking: objects are colourless.
2.0233
Two objects of the same logical form are—apart from their external properties—only distinguished from one another in that they are different.
An object is a simple but it has a logical form? The only logical forms I know of are essentially relations. It would be the relations that are composed of simples.
I suppose he might be saying that aRb and aRc represent simples in that a and b are specific instances (held constant).
May we say that objects are to atomic facts what ur elements are to some set theories?
I suppose he might be saying that aRb and aRc represent simples in that a and b are specific instances (held constant).
May we say that objects are to atomic facts what ur elements are to some set theories?
2.02331
Either a thing has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in common, and then it is quite impossible to point to any one of them.
For if a thing is not distinguished by anything, I cannot distinguish it—for otherwise it would be distinguished.
2.024
Substance is what exists independently of what is the case.
2.025
It is form and content.
2.0251
Space, time and colour (colouredness) are forms of objects.
2.026
Only if there are objects can there be a fixed form of the world.
2.027
The fixed, the existent and the object are one.
2.0271
The object is the fixed, the existent; the configuration is the changing, the variable.
2.0272
The configuration of the objects forms the atomic fact.
2.03
In the atomic fact objects hang one in another, like the links of a chain.
2.031
In the atomic fact the objects are combined in a definite way.
2.032
The way in which objects hang together in the atomic fact is the structure of the atomic fact.
2.033
The form is the possibility of the structure.
2.034
The structure of the fact consists of the structures of the atomic facts.
2.04
The totality of existent atomic facts is the world.
2.05
The totality of existent atomic facts also determines which atomic facts do not exist.
2.06
The existence and nonexistence of atomic facts is the reality.
2.061
Atomic facts are independent of one another.
2.062
From the existence or nonexistence of an atomic fact we cannot infer the existence or nonexistence of another.
2.063
The total reality is the world.
2.1
We make to ourselves pictures of facts.
2.11
The picture presents the facts in logical space, the existence and nonexistence of atomic facts.
2.12
The picture is a model of reality.
2.13
To the objects correspond in the picture the elements of the picture.
2.131
The elements of the picture stand, in the picture, for the objects.
2.14
The picture consists in the fact that its elements are combined with one another in a definite way.
2.141
The picture is a fact.
2.15
That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.
This connection of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.
2.151
The form of representation is the possibility that the things are combined with one another as are the elements of the picture.
2.1511
Thus the picture is linked with reality; it reaches up to it.
2.1512
It is like a scale applied to reality.
2.15121
Only the outermost points of the dividing lines touch the object to be measured.
2.1513
According to this view the representing relation which makes it a picture, also belongs to the picture.
2.1514
The representing relation consists of the coordinations of the elements of the picture and the things.
2.1515
These coordinations are as it were the feelers of its elements with which the picture touches reality.
2.16
In order to be a picture a fact must have something in common with what it pictures.
2.161
In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.
2.17
What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.
2.171
The picture can represent every reality whose form it has.
The spatial picture, everything spatial, the coloured, everything coloured, etc.
2.172
The picture, however, cannot represent its form of representation; it shows it forth.
2.173
The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely.
2.174
But the picture cannot place itself outside of its form of representation.
2.18
What every picture, of whatever form, must have in common with reality in order to be able to represent it at all—rightly or falsely—is the logical form, that is, the form of reality.
2.181
If the form of representation is the logical form, then the picture is called a logical picture.
2.182
Every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)
2.19
The logical picture can depict the world.
2.2
The picture has the logical form of representation in common with what it pictures.
2.201
The picture depicts reality by representing a possibility of the existence and nonexistence of atomic facts.
2.202
The picture represents a possible state of affairs in logical space.
2.203
The picture contains the possibility of the state of affairs which it represents.
2.21
The picture agrees with reality or not; it is right or wrong, true or false.
2.22
The picture represents what it represents, independently of its truth or falsehood, through the form of representation.
2.221
What the picture represents is its sense.
2.222
In the agreement or disagreement of its sense with reality, its truth or falsity consists.
2.223
In order to discover whether the picture is true or false we must compare it with reality.
2.224
It cannot be discovered from the picture alone whether it is true or false.
2.225
There is no picture which is a priori true.
Either a thing has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in common, and then it is quite impossible to point to any one of them.
For if a thing is not distinguished by anything, I cannot distinguish it—for otherwise it would be distinguished.
2.024
Substance is what exists independently of what is the case.
2.025
It is form and content.
2.0251
Space, time and colour (colouredness) are forms of objects.
2.026
Only if there are objects can there be a fixed form of the world.
2.027
The fixed, the existent and the object are one.
2.0271
The object is the fixed, the existent; the configuration is the changing, the variable.
2.0272
The configuration of the objects forms the atomic fact.
2.03
In the atomic fact objects hang one in another, like the links of a chain.
2.031
In the atomic fact the objects are combined in a definite way.
2.032
The way in which objects hang together in the atomic fact is the structure of the atomic fact.
2.033
The form is the possibility of the structure.
2.034
The structure of the fact consists of the structures of the atomic facts.
2.04
The totality of existent atomic facts is the world.
2.05
The totality of existent atomic facts also determines which atomic facts do not exist.
2.06
The existence and nonexistence of atomic facts is the reality.
2.061
Atomic facts are independent of one another.
2.062
From the existence or nonexistence of an atomic fact we cannot infer the existence or nonexistence of another.
2.063
The total reality is the world.
2.1
We make to ourselves pictures of facts.
2.11
The picture presents the facts in logical space, the existence and nonexistence of atomic facts.
2.12
The picture is a model of reality.
2.13
To the objects correspond in the picture the elements of the picture.
2.131
The elements of the picture stand, in the picture, for the objects.
2.14
The picture consists in the fact that its elements are combined with one another in a definite way.
2.141
The picture is a fact.
2.15
That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.
This connection of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.
2.151
The form of representation is the possibility that the things are combined with one another as are the elements of the picture.
2.1511
Thus the picture is linked with reality; it reaches up to it.
2.1512
It is like a scale applied to reality.
2.15121
Only the outermost points of the dividing lines touch the object to be measured.
2.1513
According to this view the representing relation which makes it a picture, also belongs to the picture.
2.1514
The representing relation consists of the coordinations of the elements of the picture and the things.
2.1515
These coordinations are as it were the feelers of its elements with which the picture touches reality.
2.16
In order to be a picture a fact must have something in common with what it pictures.
2.161
In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.
2.17
What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.
2.171
The picture can represent every reality whose form it has.
The spatial picture, everything spatial, the coloured, everything coloured, etc.
2.172
The picture, however, cannot represent its form of representation; it shows it forth.
2.173
The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely.
2.174
But the picture cannot place itself outside of its form of representation.
2.18
What every picture, of whatever form, must have in common with reality in order to be able to represent it at all—rightly or falsely—is the logical form, that is, the form of reality.
2.181
If the form of representation is the logical form, then the picture is called a logical picture.
2.182
Every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)
2.19
The logical picture can depict the world.
2.2
The picture has the logical form of representation in common with what it pictures.
2.201
The picture depicts reality by representing a possibility of the existence and nonexistence of atomic facts.
2.202
The picture represents a possible state of affairs in logical space.
2.203
The picture contains the possibility of the state of affairs which it represents.
2.21
The picture agrees with reality or not; it is right or wrong, true or false.
2.22
The picture represents what it represents, independently of its truth or falsehood, through the form of representation.
2.221
What the picture represents is its sense.
2.222
In the agreement or disagreement of its sense with reality, its truth or falsity consists.
2.223
In order to discover whether the picture is true or false we must compare it with reality.
2.224
It cannot be discovered from the picture alone whether it is true or false.
2.225
There is no picture which is a priori true.
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